If the decal is coming off backing paper but immediatly breaking up, the chances are that it's gotten brittle from age. In which case the remainder of the decals can probably be saved. MicroScale's Decal Film works very well for this or you can use a clear coat (ie Gloss Coat) sprayed on. Apply a minimum of two coats to the entire sheet, letting each coat thougherly between coats (One reason I like the MicroScale product is that you can be brushing on a 2nd coat in about 10 minutes). Since you have now made a film across the entire sheet, remember to trim as close to the decal as you can when you remove it from the sheet.
It's been my experience that when a decal won't release from the backing sheet no matter how long you let it soak, the decal is pretty much useless. It's most likely gotten damp which has activated the glue on the back and then dried and once that happens the glue won't reactivate. In that case, put the decal sheet in the round file and find a new one